Method and apparatus for measuring plasma density in processing reactors using a long dielectric tube

ABSTRACT

An apparatus for measuring plasma density of a plasma processing reactor, comprises a probe having a dielectric tube with a coaxial cable inserted therein. The coaxial cable has an open antenna tip, distance constancy is kept between the antenna tip and the dielectric tube despite varying thermal conditions. The probe can be utilized to determine resonant plasma frequency near its tip location and the corresponding plasma density.

This application is related to patent application attorney's docket number 313530-P00015 entitled “Method and Apparatus for Measuring Plasma Density in Processing Reactors using a Short Dielectric Cap”, filed concurrently herewith, the contents of which are incorporated herein in their entirety.

FIELD OF THE INVENTION

The present invention relates generally to measuring plasma density, and relates specifically to measuring plasma density in plasma processing reactors.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of an apparatus for measuring plasma density of a plasma processing reactor where a probe is moveable, according to one embodiment of the invention.

FIG. 2 is a schematic representation of an apparatus for measuring plasma density of a plasma processing reactor where a probe is not moveable, according to one embodiment of the invention.

FIG. 3 illustrates geometrical parameters of a probe 101, according to one embodiment of the invention.

FIGS. 4-5 illustrate a probe 101 utilizing an element that keeps distance constancy, according to one embodiment of the invention.

FIG. 6 illustrates a probe 101 with a dielectric tube in an alternative shape, according to one embodiment of the invention.

FIGS. 7-8 illustrate a probe 101 with alternative antenna tip shapes, according to embodiments of the invention.

FIG. 9 illustrates a probe 101 that is moveable, according to one embodiment of the present invention.

FIG. 10 is a graph illustrating resonance frequencies ω/ω_(p) versus tip distance in the m=1 mode, according to one embodiment of the invention.

DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Apparatus for Measuring Plasma Density

FIGS. 1 and 2 are schematic representations of an apparatus for measuring plasma density in a plasma processing reactor, according to one embodiment of the invention. Plasma is used in material processing reactors because it has significant advantages in processing rate, accuracy, and processing capabilities over non-plasma methods. Plasma density defines the radical content in the processing gas and the processing speed, and is important for a process engineer to know. Plasma density in a processing chamber depends on many factors, including gas composition, gas pressure, flow rate, RF power, pumping speed, geometry of the chamber, and the materials of the chamber walls and the electrodes. Plasma density in a processing chamber also depends on the power of ionizing sources, which is typically radio frequency (RF) power applied from various types of coils (i.e., inductively coupled plasma sources, or ICP), RF power applied to electrodes (i.e., capacitive coupled plasma sources, or CCP), microwave power, etc. Furthermore, plasma density in the processing chamber depends on the rate of loss of the plasma due to, for example, direct loss to the walls, the electrodes, and various recombination and neutralization processes.

In FIGS. 1 and 2, the apparatus comprises a probe 101, which comprises a coaxial cable 105 with an open antenna tip 110, surrounded by a dielectric tube 115. The coaxial cable 105 is a round, flexible, two-conductor cable consisting of, from the center outwards, a center wire, a dielectric layer, a braided metal mesh sleeve, and an outer shield. The shield prevents signals transmitted on the center wire from affecting nearby components and prevents external interference from affecting the signal carried on the antenna.

In the embodiment of FIGS. 1 and 2, the center wire extends out beyond the other layers to form open antenna tip 110. The antenna tip 110 can be straight or not straight. In one embodiment, the antenna tip can be a straight naked metal wire of at least a few millimeters long. As examples of antenna tips 110 that are not straight, see FIGS. 7 and 8, illustrating an antenna tip 110 bent in one direction, and an antenna tip 110 bent in the shape of a partial loop, respectively.

The dielectric tube 115 isolates the coaxial cable 105 and the antenna tip 110 from the plasma and prevents direct currents on the coaxial cable 105 and the antenna tip 110. The material of the dielectric tube 115 can be selected to adjust a resonant frequency for the system. The dielectric permittivity of the material of the dielectric tube 115 can thus be chosen to correspond to an expected plasma density range (e.g., quartz has a lower dielectric permittivity than ceramic). In one embodiment, a high dielectric permittivity can be used with an expected high plasma density to keep the resonant frequency within the range of the network analyzer 120 (see below) under about 5 GHz. Note that the higher the plasma density, the higher the dielectric permittivity that can be used. Possible dielectric depositions on the dielectric tube 115 in a chemically active environment do not affect the probe data, at least until the thickness of the deposition layer becomes thick enough to be comparable with the thickness of the dielectric tube 115. The tip 110 of the dielectric tube 115 is located within the area where the plasma density has to be measured. Note that spacers 305, which will be described in more detail with respect to FIG. 4 and 5, are optional.

In one embodiment, the probe 101 comprises a long dielectric tube 115 and coaxial cable 105, which can be used for scanning plasma parameters. The long dielectric tube 115 has a long coaxial cable so that the antenna tip 110 is located in a position remote from the base 135 so that the long dielectric tube 115 can detect plasma parameters in a position remote from the base 135. The base 135 can be movable, as demonstrated in FIG. 1, or stationary, as demonstrated in FIG. 2.

A base 135 closes the probe 101. In FIG. 1 where the base 135 is moveable, a flange 133 can be used to guide dielectric tube 115. Seals 134 enable the probe 101 to move relative to flange 133 and component 130. The base 135 can be made of, for example, metal (e.g., aluminum). If the probe 101 is embedded in some other structure (e.g., the substrate holder or a vacuum chamber wall, which can be metal), then the base 135 might be absent because the body of the substrate holder or vacuum chamber wall (e.g., component 130) will be the base 135. A vacuum seal can be included in base 135 to seal the probe 101.

The network analyzer 120 generates RF signals that are transmitted through the high pass filter (HPF) 125 to the probe 101. After interacting with the plasma, RF energy is reflected back through the high pass filter 125 to the network analyzer 120, providing a plasma wave resonance signature.

FIG. 3 illustrates geometrical parameters of a probe 101, according to one embodiment of the invention. The external radius of the dielectric tube 115 is a. The internal radius of the dielectric tube 115 is b. The horizontal distance between the coaxial cable end and the dielectric tube end is d. The external radius of the coaxial cable 105 is c. The radius of the antenna tip 110 is r_(a). The horizontal distance between the coaxial cable end and the antenna tip end is d_(a). The horizontal distance (i.e., the space) between the external radius of the dielectric tube 115 and the antenna tip 110 is d_(d). In one embodiment, the space is at least a few millimeters.

It is often beneficial to add elements (e.g., spacers, in-and-out feature), change elements (e.g., antenna shape), or add additional probes 101 to improve the sharpness of the absorption resonances (as shown in FIG. 10), compensate for the possible geometry modification due to heat fluxes on the probe 101 from the plasma or other sources, or gain additional information about the plasma density.

Spacers. FIG. 4 illustrates a probe 101 utilizing an element that keeps distance constancy, according to one embodiment of the invention. The distance constancy is selected so as to diminish the amplitudes of parasitic surface waves running along the dielectric tube, which otherwise might interfere with main absorption resonances used for measurements. Also, the distance constancy can help the resonant frequency to change in time with the heating of the probe due to particle and heat fluxes from the plasma. In one embodiment, a spacer can be used to keep distance constancy. The spacers are placed inside the dielectric tube 115 around the antenna tip 110 and/or the coaxial cable 105. The spacers can be in the form of tubes or rings. The spacers can be made of a dielectric material or of a metal material. In one embodiment, the spacer is a dielectric tube with an inner radius approximately equal to the radius of the antenna tip to increase constancy of the antenna tip shape under varying thermal conditions.

Spacers around the antenna tip 110 can be tubes 310, and can be made of a dielectric material to ensure relative constancy of the antenna tip distance, d_(d), in spite of possible thermal expansions of the coaxial cable 105. In addition, spacers around the antenna tip 110 ensure relative constancy of the antenna tip shape (e.g., staying straight and not being bent under varying thermal conditions).

To fix the coaxial cable 105 inside the dielectric tube 115, spacers are provided between the coaxial cable 105 and the dielectric tube 115. These spacers can be in the form of tubes or rings 305. Spacers between the coaxial cable 105 and the dielectric tube 115 can be of a dielectric material, metal material, or a combination of a dielectric material 412 with a metal material 414, as illustrated in FIG. 5. In one embodiment, the metal material 414 is used to reflect waves, so it is put against the coaxial cable. The dielectric spacer fixes the cable end at a specified position. The metal spacer provides a sharp reflecting boundary for the plasma surface waves, so the plasma absorption resonances are more clearly pronounced and measured. In one embodiment, a high dielectric permittivity can be used with an expected high plasma density to keep the resonant frequency within the frequency range of network analyzer 120, such as under about 5 GHz. Note that the higher the plasma density, the higher the dielectric permittivity that can be used.

FIG. 6 illustrates a probe 101 with a dielectric tube 115 in an alternate shape, according to one embodiment of the invention. Spacers around the antenna tip 110 can be replaced by a dielectric tube 115 of a special shape which limits cable expansion and ensures a relative constancy of the antenna tip distance, d_(d). In one embodiment, the corner of coaxial cable 105 abuts against dielectric tube 115 and antenna tip 110 extends into a portion of dielectric tube 115 with reduced diameter. With this particular shape, the probe 101 is highly sensitive to the plasma because the radial distance between the antenna tip 110 and the external surface of the dielectric tube 115 is short. The heat transfer to the antenna tip 110 increases, and thus, this type of a probe can be used with low power discharges with relatively low heat fluxes.

Note that, in one embodiment, various resonances in reflected signals are interpreted based on surface wave modes. The resonances are mapped with corresponding plasma density values around the antenna tip. Resonance modes are selected from measured absorption resonances, and the selected modes are those modes that are the strongest and also provide information about local values of the plasma density around the antenna tip. The dielectric spacer can be made of material selected to have a dielectric property used in correspondence with an expected plasma density range to produce a resonance in a desired frequency range. The material of the dielectric spacer can be chosen to have a higher dielectric permittivity for measurements in a higher plasma density range.

In one embodiment, if the coaxial cable has a smaller radius than the inner radius of the dielectric tube, and a dielectric spacer ring is provided at the end of the coaxial cable between the radius of the coaxial cable and the inner radius of the dielectric tube, the spacer ring provides more sharply emphasized boundary conditions for the surface wave reflection, making absorption resonances more pronounced. In another embodiment, the coaxial cable has a smaller radius than the inner radius of the dielectric tube, with at least one dielectric ring or short dielectric tube along the coaxial cable, surrounding the cable and located inside the dielectric tube. This provides a larger distance between the cable surface and the plasma edge and diminishes the amplitude of parasitic surface waves running along the dielectric tube, which otherwise might interfere with the main absorption resonances used for measurements.

Alternate Antenna Shapes. FIGS. 7-8 illustrate a probe 101 with alternative antenna tip shapes, according to embodiments of the invention. The alternative antenna tip shapes can be used with certain modes of resonance, corresponding to various standing wave patterns of the electromagnetic field caused by the interaction of the probe with the plasma. For example, in mode 0, the intensity is constant within a plane perpendicular to the center conductor at a constant distance from the center conductor. In mode 1, the intensity has one maximum and one minimum in the plane at a constant distance from the center conductor. In mode 2, the intensity has two maximums and two minimums in the plane at a constant distance from the center conductor.

A probe 101 with a straight antenna tip 110, as shown in FIG. 1, is beneficial for picking up the main m=0 mode of the plasma surface waves. However, other modes might be of importance as well. FIG. 7 illustrates a probe 101 with the antenna tip bent on one side, which picks up the m=1 mode of the plasma surface waves. FIG. 8 illustrates a probe 101 with the antenna tip the shape of a partial loop, which picks up the m =2 mode of the plasma surface waves.

FIG. 9 illustrates another moveable probe 750, according to one embodiment of the present invention. The components of the probe, the spacers 305 and 710, the antenna tip 110, the dielectric tube 115, and the plasma 150 are indicated on FIG. 7. Cable 706 is connected to the coaxial cable 105 by an SMA connector 745.

Feed-through bracket 727 is attached to chamber wall 760. Dielectric tube 115 extends through chamber wall in a slidable fashion as a result of vacuum seals 728. Tube 717 is attached to the end of dielectric tube 115 and spring housing 742 is attached to the end of tube 717. Spring 740 is compressed between housing 742 and SMA connector 745 to bias coaxial cable 706 and 105 into dielectric tube 115 to maintain the relative positions of antenna tip 110 and dielectric tube 115.

Dielectric tube 115, tube 717 and housing 742 can slide relative to chamber wall 760 so that the position from chamber wall 760 that probe 101 extends into the chamber can be varied. Once the desired position is obtained, screw 724 can clamp tube 717 in place. The network analyzer 720 generates RF signals that are transmitted through the high pass filter 725 to the probe 750. After interacting with the plasma, RF energy is reflected back through the high pass filter 725 to the network analyzer 720, providing a plasma wave resonance signature.

Distance constancy is kept between the antenna tip 110 and the dielectric tube tip via the spacers 710 and via the spring 740. The spring 740 allows the cable to expand when it is heated and at the same time to help the cable provide pressure against the spacers 710. This configuration is capable of providing distance constancy even where the length of the cable 105 is long, and even when the cable has significant thermal expansion due to its heating.

Method for Measuring Plasma Density

To use the probe, the frequency or wavelength at which resonance occurs is measured, which provides information needed to determine the plasma density. For example, FIG. 10 is a graph illustrating resonance frequencies ω/ω_(p) versus tip distance, according to one embodiment of the invention. The discontinuities 1401 on the graph identify the frequency at which resonance occurs. RF signals from the network analyzer 120 are reflected back to the network analyzer 120, providing the plasma wave resonance signature. The HPF 125 is located between the probe 101 and the network analyzer 120, and reduces low frequency signals which otherwise would eminate from the plasma region. As an example, a cut off frequency for the HPF can be chosen to be a factor of 10 lower than the main RF power frequency. Once the low frequency signals are cut off, the network analyzer 120 can measure the frequency or wavelength at which resonance occurs, which is related to the plasma density.

In one embodiment, a method is provided to relate observed resonances with the plasma density. Once the resonant frequency for the known wave mode is measured and the dielectric permittivity of the dielectric tube ε_(d) is known, the dielectric permittivity ε_(p) of the plasma is determined using the following dispersion relation: $\begin{matrix} {{D\left( {\omega,k_{z},m} \right)} = {{ɛ_{p} - {ɛ_{d} \cdot \frac{K_{m}\left( {k_{z}a} \right)}{K_{m}^{\prime}\left( {k_{z}a} \right)} \cdot \frac{{\alpha\quad{I_{m}^{\prime}\left( {k_{z}a} \right)}} + {\beta\quad{K_{m}^{\prime}\left( {k_{z}a} \right)}}}{{\alpha\quad{I_{m}\left( {k_{z}a} \right)}} + {\beta\quad{K_{m}\left( {k_{z}a} \right)}}}}} = 0}} & (1) \end{matrix}$

where:

ω=2πƒ (where ƒ is a wave frequency)

k_(z)=2π/λ (where k_(z) is a longitudinal wave vector; λ is a longitudinal wavelength)

m=azimuthal mode number

ε_(d)=dielectric permittivity of the dielectric tube 115

a=external radius of dielectric tube 115

b=internal radius of dielectric tube 115

I_(m)=modified Bessel function of first kind of order m

K_(m)=modified Bessel function of second kind of order m

I′_(m) and K′_(m) are derivatives, respectively, for I_(m) and K_(m).

and $\begin{matrix} {{\alpha = {\frac{1}{ɛ_{d}} \cdot \frac{{{sK}_{m}\left( {k_{z}b} \right)} - {p\quad ɛ_{d}{K_{m}^{\prime}\left( {k_{z}b} \right)}}}{{{K_{m}\left( {k_{z}b} \right)}{I_{m}^{\prime}\left( {k_{z}b} \right)}} - {{I_{m}\left( {k_{z}b} \right)}{K_{m}^{\prime}\left( {k_{z}b} \right)}}}}}{\beta = {\frac{1}{ɛ_{d}} \cdot \frac{{p\quad ɛ_{\quad d}{I_{m}^{\prime}\left( {k_{z}b} \right)}} - {{sI}_{m}\left( {k_{z}b} \right)}}{{{K_{m}\left( {k_{z}b} \right)}{I_{m}^{\prime}\left( {k_{z}b} \right)}} - {{I_{m}\left( {k_{z}b} \right)}{K_{m}^{\prime}\left( {k_{z}b} \right)}}}}}} & (2) \end{matrix}$

Parameters s and p depend on the region of the probe, particularly the antenna tip region. They are given by the expressions: $\begin{matrix} {p = {{I_{m}\left( {k_{z}b} \right)} - {\frac{I_{m}\left( {k_{z}r_{a}} \right)}{K_{m}\left( {k_{z}r_{a}} \right)}*{K_{m}\left( {k_{z}b} \right)}}}} & (3) \\ {s = {{I_{m}^{\prime}\left( {k_{z}b} \right)} - {\frac{I_{m}\left( {k_{z}r_{a}} \right)}{K_{m}\left( {k_{z}r_{a}} \right)}*{K_{m}^{\prime}\left( {k_{z}b} \right)}}}} & (4) \end{matrix}$

where r_(a)=radius of antenna tip

Once ε_(p) is known, the plasma frequency ω_(p) is determined using the following formula: $\begin{matrix} {ɛ_{p} = {1 - \frac{\omega_{p}^{2}}{\omega^{2}}}} & (5) \end{matrix}$

Once the plasma frequency ω_(p) is determined, the plasma density n_(e) can be determined using the following formula: ω_(p) √{square root over (4πn _(e) e ² /m _(e))}≈5.64×10⁴ √{square root over (n_(e))}  (6)

Once the plasma density is know at one or more points within the plasma reactor, the plasma density at any other point in the reactor can be determined using the measured value(s) and a model of relative plasma densities throughout the reactor. The model can be the result of measurements taken in the reactor or a mathematical model.

Conclusion

While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example, and not limitation. It will be apparent to persons skilled in the relevant art(s) that various changes in form and detail can be made therein without departing from the spirit and scope of the present invention. In fact, after reading the above description, it will be apparent to one skilled in the relevant art(s) how to implement the invention in alternative embodiments. Thus, the present invention should not be limited by any of the above-described exemplary embodiments.

It should also be noted that when a claim refers to “a” component, this language also covers “at least one” of that component. If a claim refers to “a” probe, an invention that includes more than one probe would necessarily include “a” probe or “one” probe.

In addition, it should be understood that the figures, which highlight the functionality and advantages of the present invention, are presented for example purposes only. The architecture of the present invention is sufficiently flexible and configurable, such that it may be utilized in ways other than that shown in the accompanying figures.

Further, the purpose of the Abstract of the Disclosure is to enable the U.S. Patent and Trademark Office and the public generally, and especially the scientists, engineers and practitioners in the art who are not familiar with patent or legal terms or phraseology, to determine quickly from a cursory inspection the nature and essence of the technical disclosure of the application. The Abstract of the Disclosure is not intended to be limiting as to the scope of the present invention in any way. 

1. An apparatus for measuring plasma density in a plasma-processing reactor, comprising: a probe comprising a coaxial cable inserted into a closed dielectric tube and having an open metal antenna tip; a coaxial cable connected to the probe; a network analyzer connected to the probe through the coaxial cable, supplying a high-frequency signal to the probe and measuring the intensity of the reflected signal; and a high-pass filter located between the coaxial cable or the probe and the network analyzer to cut off strong low frequency signals; wherein distance constancy is kept between the antenna tip and the dielectric tube; and plasma density can be measured in a chemically active environment.
 2. The apparatus of claim 1, wherein the high frequency signal is in the range of 0.5-5 GHz.
 3. The apparatus of claim 1, wherein the antenna tip is a straight naked metal wire at least a few millimeters long representing the center electrode of the coaxial cable stripped of isolation and metal screening.
 4. The apparatus of claim 3, wherein an end of the antenna tip does not touch an inner end of the dielectric tube, and there is a space of at least a few millimeters between them.
 5. The apparatus of claim 4, wherein a space between the antenna tip end and the inner end of the dielectric tube is maintained constant.
 6. The apparatus of claim 5, wherein space is maintained constant, in spite of possible thermal expansion of the coaxial cable.
 7. The apparatus of claim 6, further comprising a dielectric spacer disposed inside the main dielectric tube and placed around the antenna tip so that the space is maintained constant.
 8. The apparatus of claim 7, wherein the dielectric spacer includes a dielectric tube with an inner radius approximately equal to the radius of the antenna tip to increase constancy of the antenna tip shape under varying thermal conditions.
 9. The apparatus of claim 1, wherein various resonances in the reflected signal are interpreted based on surface wave modes.
 10. The apparatus of claim 9, wherein resonances are mapped with corresponding plasma density values.
 11. The apparatus of claim 10, wherein resonance modes are selected from the measured absorption resonances, wherein the selected resonance modes are those modes that are the strongest and also provide information about local values of the plasma density around the antenna tip.
 12. The apparatus of claim 1, wherein the dielectric tube is made of material selected to have a dielectric property used in correspondence with an expected plasma density range to produce a resonance in a frequency range of the network analyzer.
 13. The apparatus of claim 12, wherein a material with higher dielectric permittivity is chosen for the dielectric tube for measurements in a higher plasma density range to maintain the resonant frequency below about 5 GHz.
 14. The apparatus of claim 1, wherein the coaxial cable has a smaller radius than the inner radius of the dielectric tube, and a spacer ring is provided at the end of the coaxial cable between the radius of the coaxial cable and the inner radius of the dielectric tube, the ring providing more sharply emphasized boundary conditions for the surface wave reflection, making absorption resonances more pronounced.
 15. The apparatus of claim 1, wherein the coaxial cable has a smaller radius than the inner radius of the dielectric tube, and there is at least one dielectric ring or short dielectric tube along the coaxial cable, surrounding the coaxial cable, and located inside the dielectric tube, diminishing the amplitude of parasitic surface waves running along the dielectric tube, which otherwise might interfere with the main absorption resonances used for measurements.
 16. The apparatus of claim 7, wherein the dielectric spacer is metal.
 17. An apparatus for determining plasma density of plasma in a plasma processing reactor, comprising: a probe comprising a long dielectric tube and a coaxial cable inserted in the dielectric tube, the coaxial cable having an open antenna tip; wherein distance constancy is kept between the antenna tip and the dielectric tube despite varying thermal conditions.
 18. The apparatus of claim 17, wherein distance constancy is also kept between the coaxial cable and the dielectric tube despite varying thermal conditions.
 19. The apparatus of claim 17, wherein plasma density is measured in a chemically active environment.
 20. The apparatus of claim 17, further comprising a spacer proximate the antenna tip to keep the distance constancy.
 21. The apparatus of claim 18, further comprising: a spacer proximate the antenna tip to keep the distance constancy between the antenna tip and the dielectric tube; and a spacer proximate the coaxial cable to keep the distance constancy between the coaxial cable and the dielectric tube.
 22. The apparatus of claim 17, further comprising a dielectric tube spacer, an inner radius of the dielectric tube spacer being equal to or about the radius of the antenna tip, the tube spacer extending from a portion of the coaxial cable from which the antenna tip extends to the dielectric tube in the direction of the antenna tip to keep the distance constancy.
 23. The apparatus of claim 18, further comprising: a dielectric spacer; a metal spacer; or any combination thereof, disposed between the coaxial cable and the dielectric tube, to keep the distance constancy between the coaxial cable and the dielectric tube.
 24. The apparatus of claim 18, further comprising a ring spacer disposed between the coaxial cable and the dielectric tube to keep the distance constancy between the coaxial cable and the dielectric tube.
 25. The apparatus of claim 17, wherein the antenna tip is a naked metal wire representing a center electrode of the coaxial cable without isolation and/or metal screening.
 26. The apparatus of claim 17, wherein the antenna tip is straight.
 27. The apparatus of claim 17, wherein the antenna tip is not straight.
 28. The apparatus of claim 27, wherein the antenna tip bent in one direction.
 29. The apparatus of claim 17, wherein the antenna tip is bent in the shape of a partial loop.
 30. The apparatus of claim 17, wherein the shape of the antenna tip stays constant under varying thermal conditions.
 31. The apparatus of claim 17, wherein a material for the dielectric tube corresponds to an expected plasma resonant frequency.
 32. The apparatus of claim 17, wherein the dielectric tube is made of a material with a high dielectric permittivity when a high plasma density is expected to keep the resonant frequency under 3 GHz.
 33. The apparatus of claim 32, wherein the dielectric permittivity is selected so a plasma resonant frequency falls in a pre-determined range of values.
 34. The apparatus of claim 17, wherein the distance constancy kept between the antenna tip and the dielectric tube provides more sharply emphasized boundary conditions for surface wave reflection, making absorption resonances more pronounced.
 35. The apparatus of claim 17, farther comprising a base coupled to the dielectric tube.
 36. The apparatus of claim 35, wherein the base is made of dielectric material.
 37. The apparatus of claim 17, further comprising a network analyzer coupled to the probe through the coaxial cable.
 38. The apparatus of claim 37, wherein the network analyzer supplies a high-frequency signal to the probe and measures intensity of a reflected signal.
 39. The apparatus of claim 38, further comprising a high-pass filter located between and the probe and the network analyzer, the high-pass filter reducing low frequency signals.
 40. The apparatus of claim 17, wherein the distance constancy is selected so as to diminish the amplitudes of parasitic surface waves running along the dielectric tube, which otherwise might interfere with main absorption resonances used for measurements.
 41. The apparatus of claim 17, wherein the plasma density is determined around at least one probe, and the plasma density at other locations in the plasma processing reactor is determined based on the determined plasma density around the at least one probe and a model of relative plasma densities in the plasma processing reactor.
 42. A method for determining plasma density of plasma in a plasma processing reactor, comprising: utilizing a probe configured and arranged so that resonancy of a chosen mode is maximized, the probe comprising a dielectric tube and a coaxial cable inserted therein, the coaxial cable having an open antenna tip, wherein distance constancy is kept between the antenna tip and the dielectric tube despite varying thermal conditions; determining a resonant frequency or wavelength of the plasma in the plasma processing unit in the chosen mode; and determining the dielectric permittivity of the plasma using the resonant frequency or wavelength; and determining the density of the plasma using the resonant frequency or wavelength.
 43. The method of claim 42, wherein determining the resonant frequency or wavelength of the plasma in the plasma processing unit comprises: providing radio frequency signals to the probe antenna tip; receiving back reflected radio frequency signals which carry a plasma wave resonance signature; reducing strong low frequency signals; determining the resonant frequency or wavelength of the plasma waves.
 44. The method of claim 42, wherein various resonances in the reflected signal are interpreted based on surface wave modes.
 45. The method of claim 44, wherein resonances are mapped with corresponding plasma density values.
 46. The method of claim 45, wherein resonance modes are selected from the measured absorption resonances, wherein the selected resonance modes are those modes that are the strongest and also provide information about local values of the plasma density around the antenna tip.
 47. The method of claim 45, wherein the dielectric permittivity of the plasma is determined as described in the body of this patent using the dispersion relation: ${D\left( {\omega,k_{z},m} \right)} = {{ɛ_{p} - {ɛ_{d} \cdot \frac{K_{m}\left( {k_{z}a} \right)}{K_{m}^{\prime}\left( {k_{z}a} \right)} \cdot \frac{{\alpha\quad{I_{m}^{\prime}\left( {k_{z}a} \right)}} + {\beta\quad{K_{m}^{\prime}\left( {k_{z}a} \right)}}}{{\alpha\quad{I_{m}\left( {k_{z}a} \right)}} + {\beta\quad{K_{m}\left( {k_{z}a} \right)}}}}} = 0}$ where: ω=2πƒ (where ƒ is a wave frequency) k_(z)=2π/λ (where k_(z) is a longitudinal wave vector; λ is a longitudinal wavelength) m=azimuthal mode number ε_(d)=dielectric permittivity of the dielectric tube 115 a=external radius of dielectric tube 115 b=internal radius of dielectric tube 115 I_(m)=modified Bessel function of first kind of order m K_(m)=modified Bessel function of second kind of order m I′_(m) and K′_(m) are derivatives, respectively, for I_(m) and K_(m). and $\alpha = {\frac{1}{ɛ_{d}} \cdot \frac{{{sK}_{m}\left( {k_{z}b} \right)} - {p\quad ɛ_{d}{K_{m}^{\prime}\left( {k_{z}b} \right)}}}{{{K_{m}\left( {k_{z}b} \right)}{I_{m}^{\prime}\left( {k_{z}b} \right)}} - {{I_{m}\left( {k_{z}b} \right)}{K_{m}^{\prime}\left( {k_{z}b} \right)}}}}$ $\beta = {\frac{1}{ɛ_{d}} \cdot \frac{{p\quad ɛ_{\quad d}{I_{m}^{\prime}\left( {k_{z}b} \right)}} - {{sI}_{m}\left( {k_{z}b} \right)}}{{{K_{m}\left( {k_{z}b} \right)}{I_{m}^{\prime}\left( {k_{z}b} \right)}} - {{I_{m}\left( {k_{z}b} \right)}{K_{m}^{\prime}\left( {k_{z}b} \right)}}}}$ where r_(a)=radius of antenna tip
 48. The method of claim 42, wherein various resonances in the reflected signal are interpreted based on surface wave modes.
 49. The method of claim 42, wherein resonances are mapped with corresponding plasma density values.
 50. The method of claim 42, wherein resonance modes are selected from measured absorption resonances, wherein the selected resonance modes are those modes that are the strongest and also provide information about local values of the plasma density around the antenna tip.
 51. The method of claim 42, wherein the dielectric tube is made of material selected to have a dielectric property used in correspondence with an expected plasma density range to produce a resonance in a desired frequency range.
 52. The method of claim 42, wherein a material with higher dielectric permittivity is chosen for measurements in a higher plasma density range.
 53. The method of claim 42, wherein the coaxial cable has a smaller radius than the inner radius of the dielectric tube, and a spacer ring is provided at the end of the coaxial cable between the radius of the coaxial cable and the inner radius of the dielectric tube, the ring providing more sharply emphasized boundary conditions for the surface wave reflection, making absorption resonances more pronounced.
 54. The method of claim 42, wherein the coaxial cable has a smaller radius than the inner radius of the dielectric tube, and there is at least one dielectric ring or short dielectric tube along the coaxial cable, surrounding the coaxial cable, and located inside the dielectric tube, diminishing the amplitude of parasitic surface waves running along the dielectric tube, which otherwise might interfere with the main absorption resonances used for measurements.
 55. The method of claim 54, wherein the dielectric spacer is metal.
 56. The method of claim 44, wherein resonances are mapped with corresponding plasma density values.
 57. The method of claim 44, wherein resonance modes are selected from the measured absorption resonances, wherein the selected resonance modes are those modes that are the strongest and also provide information about local values of the plasma density around the antenna tip.
 58. The apparatus of claim 17, wherein the probe is slidable through a wall of the plasma processing reactor.
 59. The apparatus of claim 17, further comprising a spring coupled to the coaxial cable to bias the coaxial cable into the dielectric tube to maintain the relative positions of the antenna tip and the dielectric tip.
 60. The method of claim 42, further comprising sliding the probe through a wall in the plasma processing reactor so that the antenna tip is positioned at a desired position within the plasma processing reactor.
 61. The method of claim 42, further comprising biasing the coaxial cable into the dielectric tube to maintain the relative positions of the antenna tip and the dielectric tip.
 62. The apparatus of claim 1, wherein the probe is slidable through a wall of the plasma processing reactor.
 63. The apparatus of claim 1, further comprising a spring coupled to the coaxial cable to bias the coaxial cable into the dielectric tube to maintain the relative positions of the antenna tip and the dielectric tip.
 64. The apparatus of claim 1, wherein the dielectric tube is of a shape which limits cable expansion and helps provide a relatively constant distance between the antenna tip and the dielectric tube.
 65. The apparatus of claim 17, wherein the dielectric tube is of a shape which limits cable expansion and helps provide a relatively constant distance between the antenna tip and the dielectric tube.
 66. The method of claim 42, wherein the dielectric tube is of a shape which limits cable expansion and helps provide a relatively constant distance between the antenna tip and the dielectric tube.
 67. The apparatus of claim 64, wherein the corner of the coaxial cable abuts against the dielectric tube, and the antenna tip extends into a portion of the dielectric tube with reduced diameter.
 68. The apparatus of claim 65, wherein the corner of the coaxial cable abuts against the dielectric tube, and the antenna tip extends into a portion of the dielectric tube with reduced diameter.
 69. The method of claim 66, wherein the corner of the coaxial cable abuts against the dielectric tube, and the antenna tip extends into a portion of the dielectric tube with reduced diameter. 